why aren't the inside sides of the shape showing when I export it as a .STL file
Maybe the normals of you model are wrong. If the normal of a face is pointing inside the mesh, it may not be displayed by some renderers. When in edit mode, you can display the normals of the model using the right pane in the 3D view (section Mesh Display > normals). Try to call Make Normals Consistent (Ctrl+N) when editing your mesh.